The expression which expresses the number of square feet of wallpaper needed is 12[tex]x^{2}[/tex]-21.
Given that the length of family room is 3x, breadth be 3x , height be x and the length and breadth of door be 7 feet and 3 feet.
We are required to find the expression which shows the square feet of wallpaper needed for the walls of the family room.
Because the wallpaper is not usually used on the floor and the ceiling and on doors so we will deduct the area of ceiling , floor and door from the surface area of whole room or we will just find the area of four walls one by one and then deduct the area of door from it.
Area of four walls only=2(lh+bh)
=2(3x*x+3x*x)
=2(3[tex]x^{2}[/tex]+3[tex]x^{2}[/tex])
=2*6[tex]x^{2}[/tex]
=12[tex]x^{2}[/tex]
Area of door=length*breadth
=3*7
=21 [tex]feet^{2}[/tex]
Required area=12[tex]x^{2}[/tex]-21.
Hence the expression which expresses the number of square feet of wallpaper needed is 12[tex]x^{2}[/tex]-21.
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